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Such problems include decomposing the integer points of such sets, solving parametric integer programs, performing dependence analysis in for-loop nests and determining the validity of certain Presburger formulas. 2 January 2018 ACM Communications in Computer Algebra: Volume 51 Issue 3, September 2017 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 2,   Downloads (12 Months): 18,   Downloads (Overall): 31 Full text available: PDF The CUDA Modular Polynomial (CUMODP) Library implements arithmetic operations for dense matrices and dense polynomials, primarily with modular integer coefficients. Some operations are available for integer or floating point coefficients. Similar to other software libraries, like CuBLAS 1 targeting Graphics Processing Units (GPUs), CUMODP focuses on efficiency-critical routines and provides ... 3 July 2017 PASCO 2017: Proceedings of the International Workshop on Parallel Symbolic Computation Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 5,   Downloads (Overall): 23 Full text available: PDF We present multithreaded adaptations of the Euclidean plain division and the Euclidean GCD algorithms to the many-core GPU architectures We report on implementation with NVIDIA CUDA and complexity analysis with an enhanced version of the PRAM model. Keywords: CUDA, Euclidean division, Finite fields, Graphics processing units 4 July 2017 PASCO 2017: Proceedings of the International Workshop on Parallel Symbolic Computation Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 1,   Downloads (12 Months): 10,   Downloads (Overall): 35 Full text available: PDF Keywords: CUDA, Graphics processing units, Multithreaded programming, computer algebra 5 February 2017 ACM Communications in Computer Algebra: Volume 50 Issue 4, December 2016 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 4,   Downloads (Overall): 26 Full text available: PDF The work reported here is motivated by problems arising in solving polynomial systems over the real numbers. 6 November 2016 ACM Communications in Computer Algebra: Volume 50 Issue 3, September 2016 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 1,   Downloads (12 Months): 9,   Downloads (Overall): 71 Full text available: PDF The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over common types of coefficients (prime fields, complex rational numbers, rational functions, etc.). The code is mainly written in CilkPlus [10] targeting multicore processors. The current distribution focuses on dense polynomials ... 7 November 2016 ACM Communications in Computer Algebra: Volume 50 Issue 3, September 2016 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 1,   Downloads (12 Months): 7,   Downloads (Overall): 59 Full text available: PDF Many fundamental concepts in mathematics are defined in terms of limits and it is desirable for computer algebra systems to be able to compute them. However, limits of functions, limits of secants or topological closures are, by essence, hard to compute in an algorithmic fashion, say by doing finitely many ... 8 November 2015 CASCON '15: Proceedings of the 25th Annual International Conference on Computer Science and Software Engineering Publisher: IBM Corp. Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 0,   Downloads (12 Months): 0,   Downloads (Overall): 19 Full text available: PDF In this paper, we present the accelerator model of M eta F ork together with the software framework that allows automatic generation of CUDA code from annotated M eta F ork programs. One of the key features of this CUDA code generator is that it supports the generation of CUDA ... 9 September 2015 CASC 2015: Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301 Publisher: Springer-Verlag Bibliometrics: Citation Count: 0 For a set S of cells in a cylindrical algebraic decomposition of ℝn, we introduce the notion of generalized cylindrical algebraic formula GCAF associated with S. We propose a multi-level heuristic algorithm for simplifying the cylindrical algebraic formula associated with S into a GCAF. The heuristic strategies are motivated by ... 10 September 2015 CASC 2015: Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301 Publisher: Springer-Verlag Bibliometrics: Citation Count: 3 We outline a method for computing the tangent cone of a space curve at any of its points. We rely on the theory of regular chains and Puiseux series expansions. Our approach is novel in that it explicitly constructs the tangent cone at arbitrary and possibly irrational points without using ... Keywords: regular chain, Computational algebraic geometry, tangent cone, Puiseux series 11 September 2015 CASC 2015: Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301 Publisher: Springer-Verlag Bibliometrics: Citation Count: 2 Given a regular chain, we are interested in questions like computing the limit points of its quasi-component, or equivalently, computing the variety of its saturated ideal. We propose techniques relying on linear changes of coordinates and we consider strategies where these changes can be either generic or guided by the ... 12 August 2015 ACM Communications in Computer Algebra: Volume 49 Issue 2, June 2015 Publisher: ACM Bibliometrics: Citation Count: 0 13 February 2015 ACM Communications in Computer Algebra: Volume 48 Issue 3/4, September/December 2014 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 2,   Downloads (12 Months): 6,   Downloads (Overall): 46 Full text available: PDF The Basic Polynomial Algebra Subprograms (BPAS) provides arithmetic operations (multiplication, division, root isolation, etc.) for univariate and multivariate polynomials over prime fields or with integer coefficients. The code is mainly written in CilkPlus [11] targeting multicore processors. The current distribution focuses on dense polynomials and the sparse case is work ... 14 February 2015 ACM Communications in Computer Algebra: Volume 48 Issue 3/4, September/December 2014 Publisher: ACM Bibliometrics: Citation Count: 0 Downloads (6 Weeks): 2,   Downloads (12 Months): 9,   Downloads (Overall): 42 Full text available: PDF 15 July 2014 ISSAC '14: Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation Publisher: ACM Bibliometrics: Citation Count: 7 Downloads (6 Weeks): 2,   Downloads (12 Months): 3,   Downloads (Overall): 42 Full text available: PDF A quantifier elimination algorithm by cylindrical algebraic decomposition based on regular chains is presented. The main idea is to refine a complex cylindrical tree until the signs of polynomials appearing in the tree are sufficient to distinguish the true and false cells. We report on an implementation of our algorithm ... Keywords: regular chains, cylindrical algebraic decomposition, quantifier elimination, triangular decomposition 16 September 2013 CASC 2013: Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136 Publisher: Springer-Verlag Bibliometrics: Citation Count: 7 For a regular chain R in dimension one, we propose an algorithm which computes the (non-trivial) limit points of the quasi-component of R , that is, the set $\overline{W(R)} \setminus W(R)$ . Our procedure relies on Puiseux series expansions and does not require to compute a system ... 17 September 2012 CASC'12: Proceedings of the 14th international conference on Computer Algebra in Scientific Computing Publisher: Springer-Verlag Bibliometrics: Citation Count: 0 We consider the questions of inversion modulo a regular chain in dimension zero and of matrix inversion modulo such a regular chain. We show that a well-known idea, Leverrier's algorithm, yields new results for these questions. 18 September 2012 CASC'12: Proceedings of the 14th international conference on Computer Algebra in Scientific Computing Publisher: Springer-Verlag Bibliometrics: Citation Count: 2 As pointed out by Fulton in his Intersection Theory , the intersection multiplicities of two plane curves V ( f ) and V ( g ) satisfy a series of 7 properties which uniquely define I ( p ; f , g ) at each point p ∈ V ( ... 19 June 2012 Journal of Symbolic Computation: Volume 47 Issue 6, June, 2012 Publisher: Academic Press, Inc. Bibliometrics: Citation Count: 11 We discuss algorithmic advances which have extended the pioneer work of Wu on triangular decompositions. We start with an overview of the key ideas which have led to either better implementation techniques or a better understanding of the underlying theory. We then present new techniques that we regard as essential ... Keywords: Characteristic set, Regular chain, GCD, Resultant, Triangular decomposition 20 January 2012 ACM Communications in Computer Algebra: Volume 45 Issue 3/4, September/December 2011 Publisher: ACM Bibliometrics: Citation Count: 2 Downloads (6 Weeks): 0,   Downloads (12 Months): 3,   Downloads (Overall): 78 Full text available: PDF